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We have calculated the stellar $\beta$-decay rate of the important s-processbranching point ${}^{134}$Cs based on the state of the art shell modelcalculations. At typical $s$-process temperatures ($T\sim$ 0.2-0.3 GK), our newrate is one order of magnitude lower than the widely-used rate from Takahashiand Yokoi (hereafter TY87). The impact on the nucleosynthesis in AGB stars isinvestigated with various masses and metallicities. Our new decay rate leads toan overall decrease in the ${}^{134}$Ba/${}^{136}$Ba ratio, and well explainsthe measured ratio in meteorities without introducing the $i$ process. We alsoderive the elapsed time from the last AGB nucleosynthetic event that pollutedthe early Solar System to be $>$28 Myr based on the ${}^{135}$Cs/${}^{133}$Csratio, which is consistent with the elapsed times derived from ${}^{107}$Pd and${}^{182}$Hf. The $s$-process abundance sum of ${}^{135}$Ba and ${}^{135}$Cs isfound to increase, resulting in a smaller $r$-process contribution of${}^{135}$Ba in the Solar System.

The stellar beta-decay rate of 134Cs and its impact on the Barium nucleosynthesis in the s process